Parameterized Image Varieties: A Novel Approach to the Analysis and Synthesis of Image Sequences

Yakup Genc and Jean Ponce.

International Conference on Computer Vision, 1998. India.


Abstract

This paper addresses the problem of characterizing the space formed by all images of a rigid set of n points observed by a weak perspective or paraperspective camera. By taking explicitly into account the Euclidean constraints associated with calibrated cameras, we show that this space is a six-dimensional variety embedded in $\RR^{2n}$, and parameterize it using the image positions of three reference points. This parameterization is constructed via linear least squares from point correspondences established across a sequence of images, and it is used to synthesize new pictures without any explicit three-dimensional model. Degenerate scene and camera configurations are analyzed, and experiments with real image sequences are presented.